This challenge is pretty simple. How big can the war over the Falklands possibly be?
With a POD after 1945, How much can one wank out both the United Kingdom of Great Britain and Northern Ireland and the Argentine Republic to make the war over the Falklands as big as possible, but WITHOUT involving ANY OTHER COUNTRIES. This is too easy if Britain can call on the United States for help.
How wild could it get? Argentina striking mainland Britain is ASB, but could they mount an attack on Ascension Island? What about Argentina having better ASW abilities and causing problems for British SSNs and SSKs? Or having both of its Colossus class aircraft carriers? Or how about Sea Harriers for the Argentinian Navy? Or a more advanced Argentine Air Force?
On the flip side, could Britain have brought a full carrier to the fight? Or more than one? If so, with what aircraft? Could the Tiger class have been used to back up the Royal Marines? Or maybe Britain keeps some bigger-gunned ships around in a reserve fleet long enough to call 'em back? What about a bomber fleet and supporting tankers? TSR.2s? F-111Ks? Greater involvement by the V-bomber fleet?
Hell, considering Britain had nuclear weapons and Argentina was trying to develop them, could that war see the third nuclear bomb used in anger?
Other than the above conditions, there is no limits to this. If you can have Britain land heavy divisions in the Falklands and blow the Argentines to hell, that's usable. If you can have Argentina or Britain use covert actions against the other nation's home territory, that's OK too. Have at it, guys, and may God help us all.